$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x - 2$ and $ KL = 9x - 30$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x - 2} = {9x - 30}$ Solve for $x$ $ -4x = -28$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({7}) - 2$ $ KL = 9({7}) - 30$ $ JK = 35 - 2$ $ KL = 63 - 30$ $ JK = 33$ $ KL = 33$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {33} + {33}$ $ JL = 66$